Kinetics of the Formation of HBr

Kinetics of the Photochemical Reaction Between Hydrogen and Bromine

The photochemical combination of moist H₂ and Br₂ vapor in visible light(< 510nm) is a chain reaction and is occurs at 433-491 k.
H₂ + Br₂ ---h𝜈→ 2HBr
Possible mechanism of this photochemical reaction-
Chain Initiation-
1. Br₂ + h𝜈 ---k₁→ 2Br
Chain Propagation-
ii. Br + H₂ ---k₂→ HBr + H
iii. H + Br₂ ---k₃→ HBr + Br
Chain Inhibition-
iv. H + HBr ---k₄→ H₂ + Br
Chain Termination-
v. Br + Br ---k₅→ Br₂
where, k₁, k₂, k₃, k₄ and k₅ are rate constants.
Since HBr is formed in steps 'ii' and step 'iii' and disappear in step 'iv', hence, the net rate of formation of HBr-
d[HBr]/dt = k₂[H₂][Br] + k₃[H][Br₂] − k₄[H][HBr]  ---Eq-1
The H atom are formed in step'ii' and disappear in steps 'iii' and 'iv', hence-
d[H]/dt = k₂[Br][H₂] − k₃[H][Br₂] − k₄[H][HBr]  ---Eq-2
Applying steady state approximation, we get-
0 = k₂[Br][H₂] − k₃[H][Br₂] − k₄[H][HBr]
or, k₂[Br][H₂] = k₃[H][Br₂] + k₄[H][HBr]
The Br atoms are formed in steps 'i', 'iii' and 'iv' and disappear in step 'ii' and 'v', hence-
d[Br]/dt = k₁I_abs − k₂[Br][H₂] + k₃[H][Br₂] + k₄[H][HBr] − k₅[Br]²

Applying steady state approximation, we get-
k₁I_abs + k₃[H][Br₂] + k₄[H][HBr] = k₂[H₂][Br] + k₅[Br]²  ---Eq-3
Subtracting equation-2 from equation-3 we get-
k₁I_abs = k₅[Br]²
or, [Br] = (k₁I_abs/k₅)^1/2
Putting the value of [Br] in equation-2 we get-
k₂(k₁I_abs)^1/2[H₂] = k₃[H][Br₂] + k₄[H][HBr]


This equation agree with the experimental value. Therefore, the rate of the reaction varies with the square root of the intensity of light(I_abs).

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Related Topics

1. Quantum Yield
2. Kinetics of HCl Formation
3. Kinetics of HI Decomposition

Q. Show that the rate of reaction varies directly to the square root of the intensity of radiation absorbed.

Statement

In photochemical reactions, the rate of reaction is found to vary directly with the square root of the intensity of radiation absorbed.

Derivation

Let the intensity of radiation absorbed be denoted by I. The number of photons absorbed per unit time is proportional to I.

Number of excited molecules ∝ I

However, the rate of reaction depends on the probability of effective collisions between excited molecules. Since collisions depend on the square root of the number of excited molecules:

Rate of reaction (R) ∝ √I

Conclusion

Thus, the rate of a photochemical reaction is directly proportional to the square root of the intensity of radiation absorbed:

R ∝ √I

This relationship highlights the nonlinear dependence of reaction rate on radiation intensity in photochemical processes.